pumping wash water

I am building a darkroom that has access to water coming in, but not
going out.

It is going to be in the middle of my garage - not sharing any walls with the outside. On top of that, there are no drains in the garage.

So, my thought is to put a sizeable holding tank under the sink. In the tank
will be a sump pump that will pump the water up and out, via a hose or pipes, to a point where I can connect with the house drain system.

The least invasive/destructive route would involve pumping up to the garage attic and across to an adjoining room, then down to a drain for our clothes washer.

Home Depot sells pump setups like that for the laundry room, etc. Has tank and pump with float switch. I use one myself for my darkroom. Only problem I ever had with it was when the hose clamps rusted out and the tank overflowed instead of pumping out. It pumps up to the 11 foot ceiling with no problem.

Sounds sound. There is a design feature you might need to include. That is a "vacuum breaker" which is a modified check valve to a vent. This will allow fluid from the overhead pipe to return both to the drain and some to the sump - no problem. This prevents possible syphoning of water in your drain uncontrolled into the garage in case of a power failure - not recommended. You might be tempted to just include a forward check valve in series. I recommend against this as due to Murphy et al., it will fail when least desirable.

I love the smell of fixer in the morning. It smells like...creativity!
Truly, dr bob.

Home Depot sells pump setups like that for the laundry room, etc. Has tank and pump with float switch. I use one myself for my darkroom. Only problem I ever had with it was when the hose clamps rusted out and the tank overflowed instead of pumping out. It pumps up to the 11 foot ceiling with no problem.

I agree. I have the same set up, a 10 gal tank with a float switch. It runs on 110 V, draws very little current, pumps for 8-10 sec. every 10 gal. and makes fluids run uphill. All that you need are at the Home Depot: pump, sink drain, PVC pipe and glue. I did it myself. No leaks!